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| Ruzsa’s constant on additive functions | |
| 基金项目： | Supported by National Natural Science Foundation of China(Grant Nos.11071121and11126302);supported by Natural Science Foundation of the Jiangsu Higher Education Institutions(GrantNo.11KJB110006);the Foundation of Nanjing University of Information Science&;Technology(Grant No.20110421) |
| 摘 要： | A function f : N → R is called additive if f(mn)= f(m)+f(n)for all m, n with(m, n)= 1. Let μ(x)= max n≤x(f(n)f(n + 1))and ν(x)= max n≤x(f(n + 1)f(n)). In 1979, Ruzsa proved that there exists a constant c such that for any additive function f , μ(x)≤ cν(x 2 )+ c f , where c f is a constant depending only on f . Denote by R af the least such constant c. We call R af Ruzsa's constant on additive functions. In this paper, we prove that R af ≤ 20. |
| 关 键 词： | Additive function Ruzsa’s constant |
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